Explore topological approaches to deep learning in this 52-minute lecture by Gunnar Carlsson. Delve into TDA-inspired methods for constructing neural networks, addressing challenges like data hunger, generalization difficulties, and lack of transparency. Examine convolutional neural networks, image patch analysis, and the shape of data through topological modeling. Investigate weight space analysis for various datasets, discover geometry in convolutional situations, and explore feature space modeling. Learn about generalized convolutional nets, Klein bottle connections, and applications in microarray analysis and microbiome studies. Gain insights into learning on video and perspectives from cognitive scientist Gary Marcus.